Higher Education

An Introduction to Stochastic Processes, 1st Edition

  • Edward P.C. Kao University of Houston
  • ISBN-10: 0534255183  |  ISBN-13: 9780534255183
  • 412 Pages
  • © 1997 | Published
  • College Bookstore Wholesale Price = $300.75

About

Overview

Intended for a calculus-based course in stochastic processes at the graduate or advanced undergraduate level, this text offers a modern, applied perspective. Instead of the standard formal and mathematically rigorous approach usual for texts for this course, Edward Kao emphasizes the development of operational skills and analysis through a variety of well-chosen examples.

Table of Contents

1. INTRODUCTION
Overview / Introduction / Discrete Random Variables and Generating Functions / Continuous Random Variables and Laplace Transforms / Some Mathematical Background / Problems / Bibliographic Notes / References / Appendix
2. POISSON PROCESSES
Overview / Introduction / Properties of Poisson Processes / Nonhomogeneous Poisson Processes / Filtered Poisson Processes / Two-Dimensional and Marked Poisson Processes / Poisson Arrivals See Time Averages (PASTA) / Problems / Bibliographic Notes / References / Appendix
3. RENEWAL PROCESSES
Overview / Introduction / Renewal-Type Equations / Excess Life, Current Life, and Total Life / Renewal Reward Processes / Limiting Theorems, Stationary and Transient Renewal Processes / Regenerative Processes / Discrete Renewal Processes / Problems / Bibliographic Notes / References / Appendix
4. DISCRETE-TIME MARKOV CHAINS
Overview / Introduction / Classification of States / Ergodic and Periodic Markov Chains / Absorbing Markov Chains / Markov Reward Processes / Reversible Discrete-Time Markov Chains / Problems / Bibliographic Notes / References / Appendix
5. CONTINUOUS-TIME MARKOV CHAINS
Overview / Introduction / The Kolmogorov Differential Equations / The Limiting Probabilities / Absorbing Continuous-Time Markov Chains / Phase-Type Distributions / Uniformization / Continuous-Time Markov Reward Processes / Reversible Continuous-Time Markov Chains / Problems / Bibliographic Notes / References / Appendix
6. MARKOV RENEWAL AND SEMI-REGENERATIVE PROCESSES
Overview / Introduction / Markov Renewal Functions and Equations / Semi-Markov Processes and Related Reward Processes / Semi-Regenerative Processes / Problems / Bibliographic Notes / References / Appendix
7. BROWNIAN MOTION AND OTHER DIFFUSION PROCESSES
Overview / Introduction / Diffusion Processes / Ito's Calculus and Stochastic Differential Equations / Multidimensional Ito's Lemma / Control of Systems of Stochastic Differential Equations / Problems / Bibliographic Notes / References / Appendix / APPENDIX: GETTING STARTED WITH MATLAB / INDEX